There are many known pillow covers, used for various purposes. Many pillow covers, such as shown in U.S. Pat. No. 6,209,156, are for protecting the pillow itself from stains or soiling during use. In some cases, the cover is discarded after use, while in others, the cover may be conveniently washed. Other pillow covers, such as shown in U.S. Pat. Nos. 4,508,044, 4,165,125 and 4,480,347, are for specialized purposes, such as decoration, rebuilding of an existing pillow, or adapting a pillow for a particular use, among others. However, none of these pillow covers are directed toward the specific purpose/function of applicant's invention, i.e. a pillow cover which is useful in increasing the comfort of an existing pillow while also being adapted for use with a pouch such that the cover can itself function as a small pillow suitable for travel or similar purposes.